Problem 72 - Prealgebra

Question

If the sum of -9 and -2 is increased by 10, what number results?

Step-by-Step Solution

Answer

The result is -1.

Step 1: Calculate the Sum of the Initial Numbers

First, we need to find the sum of -9 and -2. To do this, simply add the two numbers: \(-9 + (-2) = -9 - 2 = -11\).

Step 2: Increase the Sum by 10

Now that we have the sum from the first step, which is -11, we need to increase this number by 10 to find the final result. Perform the addition \(-11 + 10\).

Key Concepts

Addition of Integers

When dealing with integers, addition can sometimes be a bit tricky, especially with negative numbers involved. An integer is a whole number that can either be positive, negative, or zero. For example: -9, 0, and 5 are all integers. Addition with integers involves combining values to get a result. Consider our example where we need to add -9 and -2 together. When adding two integers with the same sign, you keep the sign and add the absolute values.

• Here, both numbers are negative, indicating that you're moving further from zero in the negative direction.
• The absolute value of -9 is 9 and -2 is 2, so you add those: 9 + 2 = 11.

Then apply the original negative sign to your result to get -11. Thus, \(-9 + (-2) = -11\). This process is crucial for understanding integer arithmetic as it forms the base for more complex operations.

Negative Numbers

Negative numbers are simply numbers less than zero. They have a '-' sign in front of them to indicate this. In the exercise, both -9 and -2 are negative numbers.

• When dealing with negative numbers, they can represent situations where you're moving in the opposite direction on a number line-from the positive side towards the left.
• A key aspect of working with negatives is knowing that subtracting a negative is like adding a positive. This will become more intuitive with practice.

Knowing how to comfortably manage negative numbers in arithmetic operations is essential for solving problems in math efficiently.

Arithmetic Operations

Arithmetic operations are the foundation of mathematics and include addition, subtraction, multiplication, and division. Each operation has its own set of rules, particularly when negative numbers are involved.

• In addition and subtraction, you always move along the number line: left for negatives, and right for positives.
• Multiplication and division with negatives require remembering that multiplying or dividing two negative numbers gives a positive result, while a positive with a negative gives a negative result.

In our exercise, after finding the sum of -9 and -2 is -11, we added 10 to -11. Using the number line approach again: starting at -11, adding 10 moves you 10 steps to the right, resulting in -1. The fundamental understanding of arithmetic operations is valuable, as these skills are applied in various fields beyond math.